Why the supply curve of labor is likely to be upward-sloping, even if, for the economy as a whole, people work fewer hours when wage rates increase?

Due to the income effect.

Explanation:

The decision to work corresponds to the choice of how to allocate the hours of the day between work and leisure. There is therefore a trade off between work and play. The real wage corresponds to the increase in the consumption of goods for each additional hour of work, that is, the opportunity cost of leisure (how much is sacrificed from the consumption of goods for leisure). Increases in real wages, however, can have two effects on individuals' decisions: the substitution effect and the income effect. By the substitution effect, leisure is becoming relatively more expensive, decreasing the demand for leisure and increasing the labor supply. By the income effect, an increase in real wages means that individuals are richer, so they will demand more products and more leisure. The inclination of labor supply depends on which of the effects is predominant, since an increase in real wages tends to replace the effect of increasing labor supply, but the effect of income tends to decrease. Thus, the income effect can cause a drop in labor supply with rising wages.